Ban said that much of the election campaign has been conducted in a spirit of free and open competition, Xinhua quoted him as saying in a press statement.
"On the election day, it is the turn of voters to express their choice freely, according to their universal democratic rights, in an atmosphere of free of violence and intimidation," he said.
The statement said that Ban is greatly encouraged by the commitment and professionalism with which the government, the election commission and the political parties have engaged in the process, despite challenges.
The UN is committed to supporting Nepal on its path to a peaceful, prosperous and democratic future, it said.
Nepal is holding the second constituent assembly election after the first one elected in 2008 failed to promulgate a new constitution.